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Measuring Teachers- Beliefs about Mathematics: A Fuzzy Set Approach

Authors: M.A. Lazim, M.T.Abu Osman


This paper deals with the application of a fuzzy set in measuring teachers- beliefs about mathematics. The vagueness of beliefs was transformed into standard mathematical values using a fuzzy preferences model. The study employed a fuzzy approach questionnaire which consists of six attributes for measuring mathematics teachers- beliefs about mathematics. The fuzzy conjoint analysis approach based on fuzzy set theory was used to analyze the data from twenty three mathematics teachers from four secondary schools in Terengganu, Malaysia. Teachers- beliefs were recorded in form of degrees of similarity and its levels of agreement. The attribute 'Drills and practice is one of the best ways of learning mathematics' scored the highest degree of similarity at 0. 79860 with level of 'strongly agree'. The results showed that the teachers- beliefs about mathematics were varied. This is shown by different levels of agreement and degrees of similarity of the measured attributes.

Keywords: Conjoint analysis, belief, membership function, degree of similarity

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[1] Curriculum Development Centre, Ministry of Education, Malaysia. Integrated Curriculum for Secondary School, KualaLumpur: Government Publication, 2001.
[2] P. Cobb. Contexts, goals, beliefs and learning mathematics. For the Learning of Mathematics, Vol. 6, no. 2, pp. 2-9, 1986
[3] M.F. Pajeras, Teachers- beliefs and educational research: cleaning up a messy construct. Review of Educational Research, Vol. 62, pp. 307-332, 1992.
[4] P. Ernest, The impact of beliefs on the teaching of mathematics, in Bloomfield, A. and Harries, T. (Eds). Teaching and Learning in Mathematics, Derby: Association of Teachers of Mathematics. 1994.
[5] A.G. Thompson. The relationship of teachers- conceptions of mathematics and mathematics teaching to instructional practice, Educational Studies in Mathematics, Vol.15, pp. 105-127, 1984.
[6] S. Lerman. Alternative perspectives of the nature of mathematics and their influence on the teaching mathematics, British Educational Research Journal, 16, 53-61. 1990
[7] A.G. Thompson. Teachers- beliefs and conceptions: a synthesis of the research: In A.D Grouws (Ed.). Handbook of Research on Mathematics Teaching and Learning, NY: Macmillan. 1992.
[8] B. Shealy. Conceptualizing the development of two first-year secondary mathematics teachers- beliefs. Unpublished doctoral dissertation, University of Georgia, Athens, 1994.
[9] L.A. Zadeh . Fuzzy Set, Information and Control, Vol. 8, pp. 338 - 353, 1965.
[10] L.A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning, Part 1 and 2, Information Sciences, Vol. 8, pp. 199- 249, pp. 301- 357, 1975
[11] H.J. Zimmerman. Fuzzy Sets Theory and its applications (2nd revised ed.). Boston: Kluwer Academics Publishers, 1991.
[12] C.C. Ragin. Fuzzy Set Social Science. Chicago: Chicago Univ Press, 2000.
[13] K. Asai,. Fuzzy Systems for Management. Amsterdam: IOS Press, 1995.
[14] G.Bojadziev and ,M. Bojadziev. Fuzzy Logic for Business, Finance and Management. Singapore; World Scientific, 1997.
[15] S. Weon, and J. Kim. Learning achievement evaluation strategy using fuzzy membership function, 31st ASEE/IEEE Frontiers in Education Conference, Reno: NV, 2001.
[16] P.E. Green, and V. Srinivasan. Conjoint analysis in market research: New developments and directions, Journal of Marketing, Vol. 54, pp. 3- 19, 1990.
[17] I.B.Turksen, and I.A. Willson.. A fuzzy set preference model for consumer choice. Fuzzy Sets and Systems, Vol. 68, pp. 253- 353, 1994.
[18] G. Carter, and K. S. Norwood, The relationship between teacher and student beliefs about mathematics. School Science and Mathematics, Vol. 97, no. 2, pp. 62-67, 1997.
[19] D.R. Wittink and P Cattin, Commercial use of conjoint analysis: An update, Journal of Marketing, Vol. 53, pp. 91-96, 1989.
[20] R. Borasi, The invisible hand operating in mathematics instruction: Students- Conceptions and Expectations. Teaching and Learning Mathematics in the 1990s. Reston, VA: NCTM, 1990.
[21] C.S. Lim. A study on Malaysian Mathematician-s way of knowing. Report on Short Term Research Grant, Penang: Universiti Sains Malaysia Press, 2002.
[22] C.S. Lim. Public Images of Mathematics. Unpublished Ph.D thesis, University of Exeter, UK, 1999.
[23] A.G. Thompson. Teachers- beliefs and conceptions: a synthesis of the research, in A.D Grouws (Ed.). Handbook of Research on Mathematics Teaching and Learning, NY: Macmillan, 1992.
[24] S. Perdikaris,. Mathematizing the Van Hiele levels: a fuzzy set approach, International Journal of Mathematics Education and Science Technology, Vol. 27, no. 1, pp. 41-47, 1996.
[25] C.S. Crowther, W.H. Batchelder, and X. Hu, Measurement -theoretic analysis of fuzzy logic model of perception, Psychological Review, Vol. 102, no. 2, pp. 396-408, 1995.
[26] M. A. Lazim, Construction of conceptual knowledge of quadratic functions in QFtica: A fuzzy approach and multiple representations. Unpublished Ph.D thesis, University College of Science and Technology, Malaysia, 2004.
[27] M.A. Lazim, W.A. Salihin, and M.T. Abu Osman, Fuzzy sets in the social sciences: An overview of related research, Jurnal Teknologi, Vol.41, no.E, pp.43-54, 2004.